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Master's Dissertation
DOI
https://doi.org/10.11606/D.76.2020.tde-27052020-191622
Document
Author
Full name
Matheus Goulart Barbosa
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2020
Supervisor
Committee
Vanzela, Daniel Augusto Turolla (President)
Landulfo, Andre Gustavo Scagliusi
Saa, Alberto Vazquez
Title in English
Thermodynamic properties of causal horizons
Keywords in English
Black hole thermodynamics
Causal horizons
Lightlike hypersurfaces
Abstract in English
Black hole thermodynamics emerged as a surprising connection between thermodynamics and general relativity, showing that one may attribute properties like entropy and temperature to a black hole´s event horizon. Inspired by it, studies from the last decades indicate that this analogy extends itself to many models and systems in which one considers the existence of causal horizons. Given certain assumptions, it is even possible to derive Einstein´s field equations from the laws of thermodynamics. Nevertheless, this result was not constructed on foundations so solid as those of black hole thermodynamics, leaving room for a formalization of these ideas. Therefore, in order to advance in the generalization of the relation between thermodynamics and gravitation, one may focus on the study of the geometry of causal horizons, which correspond to lightlike hypersurfaces of a spacetime. In this work, we review the laws of black hole thermodynamics, giving special attention to the generalized second law, and show how the mentioned analogy is formulated for general causal horizons. Then, we present the induced geometric objects on lightlike hypersurfaces, providing the basic mathematical tools to analyze the geometry of causal horizons.
Title in Portuguese
Propriedades termodinâmicas de horizontes causais
Keywords in Portuguese
Hipersuperfícies tipo-luz
Horizontes causais
Termodinâmica de buracos negros
Abstract in Portuguese
A termodinâmica de buracos negros surgiu como uma surpreendente conexão entre termodinâmica e relatividade geral, mostrando que é possível atribuir propriedades como entropia e temperatura ao horizonte de eventos de um buraco negro. Inspirados por ela, estudos feitos nas últimas décadas indicam que esta analogia se estende para muitos modelos e sistemas nos quais é considerada a existência de horizontes causais. Dadas certas suposições, é possível inclusive derivar as equações de campo de Einstein a partir das leis da termodinâmica. Contudo, tal resultado não foi construído sobre bases tão sólidas quanto aquelas da termodinâmica de buracos negros, abrindo espaço para uma formalização destas ideias. Desta forma, a fim de avançar na generalização da relação entre termodinâmica e gravitação, é possível focar no estudo da geometria de horizontes causais, os quais correspondem a hipersuperfícies tipo-luz de um espaço-tempo. Neste trabalho, serão revisadas as leis da termodinâmica de buracos negros, dando atenção especial para a segunda lei generalizada, e será mostrado como a analogia mencionada é formulada para horizontes causais genéricos. Em seguida, serão apresentados os objetos geométricos induzidos em hipersuperfícies tipo-luz, fornecendo as ferramentas matemáticas básicas para analisar a geometria de horizontes causais.
 
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Publishing Date
2020-05-28
 
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